by Jie Hu, Email: jie.hu.ds@gmail.com

This markdown will use explorsive data analysis to figure out which attributes affect quality of red wine significantly. To do this, I use the dataset including the quality rate by at least 3 experts and the chemical properties of the wine. This dataset might indicate how current experts, representing the test nowadays, think what a good red wine is.

Univariate Plots Section

Explore part

To begin with, let’s summarise the data:

## 'data.frame':    1599 obs. of  12 variables:
##  $ fixed.acidity       : num  7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
##  $ volatile.acidity    : num  0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
##  $ citric.acid         : num  0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
##  $ residual.sugar      : num  1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
##  $ chlorides           : num  0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
##  $ free.sulfur.dioxide : num  11 25 15 17 11 13 15 15 9 17 ...
##  $ total.sulfur.dioxide: num  34 67 54 60 34 40 59 21 18 102 ...
##  $ density             : num  0.998 0.997 0.997 0.998 0.998 ...
##  $ pH                  : num  3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
##  $ sulphates           : num  0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
##  $ alcohol             : num  9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
##  $ quality             : int  5 5 5 6 5 5 5 7 7 5 ...

The dataset includes 1599 observations with 12 variables.

Then let’s explot the variables one by one. Because all the variables are numeric, I will mainly use histogram to explore and figure out if there’re something interesting worth further steps.

- quality -

Quality is what this report concerns with, the rate here represent average rate from at least 3 experts. First let’s see how the quality of 1599 wine distributed.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.000   5.000   6.000   5.636   6.000   8.000
## 
##   3   4   5   6   7   8 
##  10  53 681 638 199  18

Quality, ranging from 3-8, is integer type data. About 82.5% observations get 5-6 ratings, while only 14.2% (227 counts) got 3,7 or 8 scores on quality rating. Because the score were average made by 3 or more experts and I assume it’s trustworthy.

-fixed.acidity-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    4.60    7.10    7.90    8.32    9.20   15.90

“fixed.acidity” is a measure of inside liquid concentration. The histogram a little right-skewed distributed with some outliers located at right side. The most frequent values are between 7-8. IQR is 2.1.

-volatile.acidity-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1200  0.3900  0.5200  0.5278  0.6400  1.5800

“volatile.acidity” is measure of acidity above-surface of liquid. The histogram is right-skewed distributed with some outliers located at right side. The most frequent values are between 0.4-0.6. IQR is 0.25.

-citric.acid-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.090   0.260   0.271   0.420   1.000

“citric.acid” is right-skewed distributed with some outliers located at right side. The most frequent values 0. It’s also interesting a lot of wine have citric.acid = 0, IQR is 0.33.

-residual.sugar-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.900   1.900   2.200   2.539   2.600  15.500

“residual.sugar” is right-skewed distributed with a lot of outliers located at right side. The most frequent values are between 1.9-2.4. IQR is 1.7.

-chlorides-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01200 0.07000 0.07900 0.08747 0.09000 0.61100

“chlorides” is right-skewed distributed with a lot of outliers located at right side. The most frequent values are between 0.062-0.112. IQR is 0.02.

-free.sulfur.dioxide-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    7.00   14.00   15.87   21.00   72.00

“free.sulfur.dioxide” is right-skewed distributed with a lot of outliers located at right side. The most frequent values are between 5-8. IQR is 14. Notice the number of free sulfur is larger than other ingredients like acidity, it’s because of different unit is applied. Sulfur is using \(g/dm^3\), while acidity variables are using \(mg/dm^3\). Actually, wine contains much less sulfur (free or total) than other ingredients.

-total.sulfur.dioxide-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    6.00   22.00   38.00   46.47   62.00  289.00

“total.sulfur.dioxide” is right-skewed distributed with some outliers located at right side. The most frequent values are between 15-25. IQR is 40. Notice wine contains a log of total sulfur dioxide being compared with other ingredients, even more than free sulfur. It’s reasonable total sulfur should be more than free sulfur because conceptually, free sulfur is part of total surful.

-density-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9901  0.9956  0.9968  0.9967  0.9978  1.0040

“density” is approximately symmetric, and it’s surprising the difference among different wines, though they might test significantly different, are not that big.

-pH-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.740   3.210   3.310   3.311   3.400   4.010

“pH” is almost symmetric. The most frequent value is between 3.24 and 3.44, IQR is 0.19. It’s not a big difference. But one thing interests is that what’s the quality of the wines with lowest and most value of pH? Will be discussed later.

-sulphates-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3300  0.5500  0.6200  0.6581  0.7300  2.0000

“sulphates” is right-skewed distributed with some outliers located at right side. The most frequent values are between 0.5-0.7. IQR is 0.18.

-alcohol-

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.40    9.50   10.20   10.42   11.10   14.90

“alcohol” is right-skewed distributed with some outliers located at right side. The most frequent values are between 9.4-9.6. IQR is 1.6.

Question answer part

What is the structure of your dataset?

The red wine quality dataset include 1599 observations and 12 variables. All attributes are numeric, 11 of them are continuous test result and 1, the quality, is rating of integers ranging from 3 to 8. It’s pretty tidy and none of attributes have NA values.

What is/are the main feature(s) of interest in your dataset?

After take a look at the attributes of the dataset, I found the variables like pH, alcohol, sulphates etc. most interesting to me, because I leared some red wine quality determinant before and do hope to explore how these variables distributed and how they related to wine quality.

What other features in the dataset do you think will help support your investigation into your feature(s) of interest?

By the above correlation matrix, volatile.acidity, sulphates and alcohol are the attributes most coorelated with quality of wine. Thus, these 3 attributes are most attractive to me.

Did you create any new variables from existing variables in the dataset?

I haven’t create any new features so far. But I will create in below analysis.

Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?

All attributes have outliers with extreme value. So far I haven’t remove any data because I want to keep all data in first stage. The next step, when I look into relationship between 2 attributes, I will remove outliers if necessary.

Bivariate Plots Section

Then I create correlation matrix to figure out which attributes are worth further exploring.

From this plot, we can see some pair of attributes associate with each other. For example, citric.acidity associates positively with fixed.acidity, while pH negatively associates with fixed.acidity. However, there seems no attributes have strong correlation with quality.

Here, alcohol, volatile.acidity, sulphates are top3 attributes that associated with quality. So let’s explore further on quality and these 3 variables.

Now let’s explore how these 3 attributes interact with quality.

-quality vs. alcohol-

It seems there’s positive relationship between alcohol and quality. High quality wines are more likely to have high percentage of alcohol. The corelation coeffecient \(R^2 = 0.2263\), which means alcohol can explain only 22.63% the variation of quality.

## 
## Call:
## lm(formula = alcohol ~ quality, data = wine_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.2517 -0.6233 -0.2233  0.5483  4.8767 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.88160    0.16532   41.62   <2e-16 ***
## quality      0.62835    0.02904   21.64   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9374 on 1597 degrees of freedom
## Multiple R-squared:  0.2267, Adjusted R-squared:  0.2263 
## F-statistic: 468.3 on 1 and 1597 DF,  p-value: < 2.2e-16

-quality vs. volatile.acidity-

To avoid overplotting, I add transparency in this plot

Now we can see a negative association between these two attributes. While alcohol is increasing with quality, volatile acidity is negatively associated with quality. The corelation coeffecient \(R^2 = 0.152\), which means volatile.acidity can explain only 15.2% the variation of quality.

## 
## Call:
## lm(formula = quality ~ volatile.acidity, data = wine_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.79071 -0.54411 -0.00687  0.47350  2.93148 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       6.56575    0.05791  113.39   <2e-16 ***
## volatile.acidity -1.76144    0.10389  -16.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7437 on 1597 degrees of freedom
## Multiple R-squared:  0.1525, Adjusted R-squared:  0.152 
## F-statistic: 287.4 on 1 and 1597 DF,  p-value: < 2.2e-16

-sulphates vs. quality-

We can see a positive association between these two attributes. The corelation coeffecient \(R^2 = 0.06261\), which means sulphates can explain only 6.26% the variation of quality.

## 
## Call:
## lm(formula = quality ~ sulphates, data = wine_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2432 -0.5424  0.1102  0.4456  2.3977 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.84775    0.07842   61.82   <2e-16 ***
## sulphates    1.19771    0.11539   10.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7819 on 1597 degrees of freedom
## Multiple R-squared:  0.0632, Adjusted R-squared:  0.06261 
## F-statistic: 107.7 on 1 and 1597 DF,  p-value: < 2.2e-16

From the matrix, we can also see there’re corelated attributes:

This positive association can be due to the fact that citric acid provides solid support to fixed acidity.

Volatile acid, however, is negatively associated with citric acid because citric acid rarely volatilize. You can test it but can hardly smell.

Acidity inside liquid, the wine, will certaily decrease pH. The smaller the value of pH is, the liquid becomes more acid.

Acidity is provided by acid mocules with heavier weight than water and alcohol because these acid moleculars are resolved as ions wondering among the space of water moleculars.

Next, there’re some questions I’m interested in.

  1. How’s quality of wine with no citric.acid Recall that we find there’s over 150 observations with citric.acid value equal to 0, we have adequate data to explore:

The distribution is quite similar to overall wine data. Now let’s make boxplots to compare the quality of two groups: with/without citric acid.

Though the median is different, the plots looks quite similar. Whether having citric acid seems do not affect quality significantly.

  1. How pH without or without citric acid? And how’s quality of wines with the most extremely acid pH?

We can see the wines with citric acid have lower pH. But we don’t know if extreme pH will affect quality. If yes, citric acid can be a indirect factor to improve quality of wine, because from the above correlation matrix, we can see, beside fixed acid, citric is the biggest factor associates with pH.

## 
## FALSE  TRUE 
##  1570    29

There’re 29 wines with pH less than 3 (A strong acid level!).

This is really frustrating. :( However, we learn extreme pH doesn’t affect quality that much.

  1. Are wines with higher residual sugar indicating lower quality?

“Sweetness is happiness!”

According to our experience, food with more sugar will be more attractive. Like cake, cola, and even some of the sweet wines. Does this happen in red wine?

Let’s compare quality by cut data into different level of residual sugar, and then plot quality boxcharts in gourp of sugar level:

The plot tells us the relationship between sugarlevel and quality is not very strong. From the correlation, we can draw same conclusion.

## [1] 0.01373164

Let’s refresh these interesting discoveries in this section: - Increasing fixed.acidity will lead to decreasing pH because more hydrogen ion appears - Citric.acidity is a kind of acid without volatile, so it’s reasonable when citric.acidity increase, fixed acidity will increase. As total acidity is divided into two groups, namely the volatile acids and the nonvolatile or fixed acids. So it’s reasonable when Citric.acidity increases, volatile will decrease - when the total amount of acid increases, density will increase because water molecule is much lighter than these acid ion - Whether having citric acid is not a significant indicator of quality - Extreme pH is not an indicator of wine quality - Residual sugar is not a significant indicator, too

Bivariate Analysis

Before further analysis, it’s necessary to remove outliers because these outliers might bias our model. Because data are distributed right-skewed in the dimentions of these 3 attrbutes, I will remove top 1% data.

##  volatile.acidity   sulphates         alcohol     
##  Min.   :0.1200   Min.   :0.3300   Min.   : 8.40  
##  1st Qu.:0.3900   1st Qu.:0.5500   1st Qu.: 9.50  
##  Median :0.5200   Median :0.6200   Median :10.10  
##  Mean   :0.5218   Mean   :0.6493   Mean   :10.39  
##  3rd Qu.:0.6350   3rd Qu.:0.7200   3rd Qu.:11.03  
##  Max.   :1.0100   Max.   :1.2600   Max.   :13.30

After this, I removed 52 observations. Now we have the data which has all maximum of 3 main attributes close to its 3rd quantile. The correlation between quality and one of the main attributors are:

##                        [,1]
## volatile.acidity 0.13475395
## sulphates        0.09393676
## alcohol          0.23549438

Now, I apply the model:

## 
## Calls:
## m1: lm(formula = quality ~ alcohol, data = wine_data.improved)
## m2: lm(formula = quality ~ alcohol + volatile.acidity, data = wine_data.improved)
## m3: lm(formula = quality ~ alcohol + volatile.acidity + sulphates, 
##     data = wine_data.improved)
## 
## =====================================================
##                        m1         m2         m3      
## -----------------------------------------------------
##   (Intercept)        1.721***   2.879***   2.227***  
##                     (0.181)    (0.195)    (0.206)    
##   alcohol            0.377***   0.331***   0.319***  
##                     (0.017)    (0.017)    (0.017)    
##   volatile.acidity             -1.298***  -1.066***  
##                                (0.102)    (0.104)    
##   sulphates                                1.012***  
##                                           (0.121)    
## -----------------------------------------------------
##   R-squared             0.235      0.307      0.337  
##   adj. R-squared        0.235      0.307      0.336  
##   sigma                 0.691      0.658      0.643  
##   F                   475.914    342.767    261.977  
##   p                     0.000      0.000      0.000  
##   Log-likelihood    -1621.453  -1544.961  -1510.723  
##   Deviance            736.898    667.514    638.611  
##   AIC                3248.905   3097.922   3031.446  
##   BIC                3264.938   3119.299   3058.166  
##   N                  1547       1547       1547      
## =====================================================

Even the linear model with all 3 most significant predictors, it can count for roughtly 33.7% the variation on quality.

Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?

Features like alcohol, volatile.acidity and sulphates have relatively stronger (though below moderate level), while other attributes have quite small or even nearly no relationship with quality.

The pH analysis and citric analysis parts are both frustrating to me, I find both are not significant indicators to wine quality even with extreme values. This is to my great surprise.

Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?

Yes, I listed 4 pairs of corelated attributes in above analysis: 1. citric.acid ~ fixed.acidity, positively associated 2. citric.acid ~ volatile.acidity, negatively associated 3. fixed.acidity ~ pH, negatively associated 4. density ~ fixed.acidity, positively associated

What was the strongest relationship you found?

pH and fixed acidity is the pair with strongest relationship (\(R = -0.68\)) I found.

Besides, 2 pairs have strong relationship with \(R = 0.67\): citric.acid ~ fixed.acidity and density ~ fixed.acidity

All these three pairs reach moderate level of association.

Multivariate Plots Section

Before doing plot, I firstly make quality as factor with levels “Low”(1-3), “Moderate”(4-6), “High”(7-8). And because the moderate quality has much more variation, here I only consider low/high quality in plots of this section.

There’s apparent pattern that high quality wine will more likely to fall into bottom right side of this graph, which means higher alcohol level plus lower volitile acidity will likely to indicate a better red wine.

Now I will exam another 4 groups of attributes of great interests (Want to check if anecdotes I heard are right):

This plot indicate that low quality red wines are more likely to have higher pH and high density together. Though this difference might not be obvious.

Under the conclusion that chlorides doesn’t affect quality, high quality wines are more likely to have high sulphates. The reason is that sulphates is preservative which can maintain a wine’s freshness because of its antioxidant and antibacterial properties.

As residual sugar doesn’t affect quality, alcohol is main indicator of wine quality - higher-quality wines are more likely having higher percentage alcohol.

As chlorides doesn’t affect quality a lot, higher-quality wines are more likely to have higher fixed acidity.

-Quality, Citric Acid and Density-

Citric Acid and Density are the 2 most significant indicators for quality. Here I plot them together. From the chart we can see higher-quality wines are more likely to have higher density and citric acid together, which proof my conclusion above.

Multivariate Analysis

Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?

From these plots, we can see: - Higher pH, higher sulphates, higher alcohol and higher fixed acidity are more likely to indicate red wines with higher quality - it’s hard to judge quality by density, chlorides and residual sugar values

Were there any interesting or surprising interactions between features?

It’s surprising these pairs of attributes are almost independent to each other, we can either see horizontal / vertical pattern or the data point massed up.

OPTIONAL: Did you create any models with your dataset? Discuss the strengths and limitations of your model.

Yes, in above analysis, I created a linear model to see how the attributes like alcohol, sulphates, and volatile.acidity interact with quality.

The pros of this model include: - it’s straightforward and self-explained what kind of wine will be with high quality - easy to plot and predict

However, there’re cons: - even with most significant attributes, the model can explain only 33.6% variation of quality, which means over 66.3% variation is out of control, which might make this model unreliable - the data is distributed in a very complicated pattern, applying linear model might be a naive choice to get rid of too much information

To better improve the result, both advanced model technics and more dimentional data are required, for example, how each score of quality such red wine gets.

Final Plots and Summary

Plot One

From above analysis, we can see alcohol is the strongest attribute to predict quality. To better show this positive association, here I add mean, median, quatile line to above plot.

Description One

From the plot, we can see though the data is lying everywhere, there’s a pattern can be drawn that the quality of red wine will increase with alcohol percentage.

Plot Two

From the discussion on correlated attributes, I found, density is highly positively associated with fixed.acidity and residual.sugar, meanwhile highly negatively associates with alcohol, so now let’s see if density can be expressed as combination of these 3 attributes:

Description Two

Here, \(R^2\) of above pair is:

## [1] 0.5990392

It’s pretty high! One of possible explaination can be: - alcohol has much lower density than water and acid so increase alcohol will decrease density - fixed acidity and residual sugar will both contribute to increase density because they are heavy than water/alcohol

Plot Three

The plot that quality is associated with volatile.acidity has data dispersed, it might be hard to figure out pattern, but I can draw some statistics conclusion if based on probability.

Description Three

From such plot, we can see high quality red wine tends to have more probability of low volitile acidity. So if a red wine has strong acid smell, it possibly a low-quality red wine.

Reflection

In this report, I firstly explore all attributes by their distributions and list the questions I’m interested in. For example, can sweetness, pH and citric acid improve quality?

Then, in bivarate analysis part, I create correlation matrix, select the most 3 significant attributes (alcohol, sulphates, volatile.acidity) associated with quality, and then explore how the data distributes along these 3 attribute dimentions. I find out by histogram and boxplot that data are right skewed distributed along these 3 dimension respectively. To answer my concerns: if sweetness, pH and citric acid can improve quality, I explore the relationship one by one.

Next, I plot how these 3 attributes associate with quality by scatter plot and linear model lines: - in alcohol vs. quality plot and sulphates vs. quality plot, I find both have positive association - in volatile.acidity, I find negative association I use jitter and set transparency to improve the data visualization. Besides, I use linear model to check how these 3 attributes can be fitted by data and then plot 4 scatter plot with different combination to see the strongest associate between attributes.

Furthermore, I use leveled scatter plot to get idea how quality level distributed in different attributes’ dimension scales and reach the assersion: Higher pH, higher sulphates, higher alcohol and higher fixed acidity are more likely to indicate red wines with higher quality.

Finally, I use stacked bar plot to show that higher quality level wine tends to have less probability to involve big volatile acidity value.

Forecast

This red wine dataset has 12 attributes messed up. Explorasive data analysis does provide with an efficient way to capture idea. But to improve the accuracy of predicting quality of red wine, we can try more improvements, including: - improve the data, with more data on low / high quality of wines, and more detailed description on how the quality score were given. Better involve more features, like the year of harvest, brew time, location of Vineyard and so on - use machine learning, like SVM / Decision Tree to mine more details of attributes in more advanced dimensional vision

Reference